Statistical scale-up of 3D particle-tracking simulation for non-Fickian dispersive solute transport modeling

Numerical techniques for subsurface flow and transport modeling are often limited by computational limitations including fine mesh and small time steps to control artificial dispersion. Particle-tracking simulation offers a robust alternative for modeling solute transport in subsurface formations. However, the modeling scale usually differs substantially from the rock measurement scale, and the scale-up of measurements have to be made accounting for the pattern of spatial heterogeneity exhibited at different scales. Therefore, it is important to construct accurate coarse-scale simulations that are capable of capturing the uncertainties in reservoir and transport attributes due to scale-up. A statistical scale-up procedure developed in our previous work is extended by considering the effects of unresolved (residual) heterogeneity below the resolution of the finest modeling scale in 3D. First, a scale-up procedure based on the concept of volume variance is employed to construct realizations of permeability and porosity at the (coarse) transport modeling scale, at which flow or transport simulation is performed. Next, to compute various effective transport parameters, a series of realizations exhibiting detailed heterogeneities at the fine scale, whose domain size is the same as the transport modeling scale, are generated. These realizations are subjected to a hybrid particle-tracking simulation. Probabilistic transition time is considered, borrowing the idea from the continuous time random walk (CTRW) technique to account for any sub-scale heterogeneity at the fine scale level. The approach is validated against analytical solutions and general CTRW formulation. Finally, coarse-scale transport variables (i.e., dispersivities and parameterization of transition time distribution) are calibrated by minimizing the mismatch in effluent history with the equivalent averaged models. Construction of conditional probability distributions of effective parameters is facilitated by integrating the results over the entire suite of realizations. The proposed method is flexible, as it does not invoke any explicit assumption regarding the multivariate distribution of the heterogeneity. In contrast to other hierarchical CTRW formulation for modeling multi-scale heterogeneities, the proposed approach does not impose any length scale requirement regarding sub-grid heterogeneities. In fact, it aims to capture the uncertainty in effective reservoir and transport properties due to the presence of heterogeneity at the intermediate scale, which is larger than the finest resolution of heterogeneity but smaller than the representative elementary volume, but it is often comparable to the transport modeling scale.     

A case study of spatial heterogeneity of soil moisture in the Loess Plateau, western China： A geostatistical approach

Soil moisture distribution shows highly variation both spatially and temporally. This study assesses the spatial heterogeneity of soil moisture on a hill-slope scale in the Loess Plateau in West China by using a geostatistical approach. Soil moisture was measured by time-domain reflectometry （TDR） in 313 samples. Two kinds of sampling scales were used （2 × 2 m and 20 ×20 m） at two soil layers （0-30 cm and 30-60 cm）. The general characteristics of soil moisture were analyzed by a classical statistics method, and the spatial heterogeneity of soil moisture was analyzed using a geostatistical approach. The results showed that the spherical model is the best-fit model to simulate soil moisture on the experimental hill-slope. The parameters of this model indicated that the spatial dependence of soil moisture in the selected hill-slope was moderate. Even the 2 × 2 m sampling scale was too coarse to show the detailed spatial variances of soil moisture in this area. The dependent distance increased from 27.4 m to 494.16 m as the sampling scale became coarse （from 2× 2 m to 20 ×20 m）. A map of soil moisture was generated by using original soil moisture data and interpolated values determined by the Kriging method. The average soil moisture （area weighted） in the different layers of soil was calculated on the basis of this map （10.94% for the 0-30 cm soil layer, 11.88% for the 30-60 cm soil layer）. This average soil moisture is lower than the corresponding average effective soil moisture, which suggests that the soil moisture is not sufficient to support vegetation in this area.     

Beerkan multi-runs for characterizing water infiltration and spatial variability of soil hydraulic properties across scales

A method is presented for characterizing the spatial variability of water infiltration and soil hydraulic properties at the transect and field scales. The method involves monitoring a set of 10 Beerkan runs distributed over a 1-m length of soil, and running BEST (Beerkan estimation of soil transfer parameters) methods to derive hydraulic parameters. The Beerkan multi-runs (BMR) method provides a significant amount of data at the transect scale, allowing the determination of correlations between water infiltration variables and hydraulic parameters, and the detection of specific runs affected by preferential flow or water repellence. The realization of several BMRs at several transects on the same site allows comparison of the variation between locations (spatial variability at the field scale) and at the transect scale (spatial variability at the metre scale), using analysis of variance. From the results, we determined the spatial variability of water infiltration and hydraulic parameters as well as its characteristic scale (transect versus field).     

Influence of heterogeneity on unsaturated hydraulic properties: (1) local heterogeneity and scale effect

Spatial heterogeneity is ubiquitous in nature, which may significantly affect the soil hydraulic property curves. The models of a closed‐form functional relationship of soil hydraulic property curves (e.g. VG model or exponential model) are valid at point or local scale based on a point‐scale hydrological process, but how do scale effects of heterogeneity have an influence on the parameters of these models when the models are used in a larger scale process? This paper uses a two‐dimensional variably saturated flow and solute transport finite element model (VSAFT2) to simulate variations of pressure and moisture content in the soil flume under a constant head boundary condition. By changing different numerical simulation block sizes, a quantitative evaluation of parameter variations in the VG model, resulting from the scale effects, is presented. Results show that the parameters of soil hydraulic properties are independent of scale in homogeneous media. Parameters of α and n in homogeneous media, which are estimated by using the unsaturated hydraulic conductivity curve (UHC) or the soil water retention curve (WRC), are identical. Variations of local heterogeneities strongly affect the soil hydraulic properties, and the scale affects the results of the parameter estimations when numerical experiments are conducted. Furthermore, the discrepancy of each curve becomes considerable when moisture content becomes closer to a dry situation. Parameters estimated by UHC are totally different from the ones estimated by WRC. Copyright © 2012 John Wiley & Sons, Ltd.     

Inferring Heterogeneity in Aquitards Using High-Resolution δD and δ18O Profiles

Vertical depth profiles of pore water isotopes (δD and δ¹⁸O) in clay-rich aquitards have been used to show that solute transport is dominated by molecular diffusion, to define the timing of geologic events, and to estimate vertical hydraulic conductivity. The interpretation of the isotopic profiles in these studies was based on pore water samples collected from piezometers installed in nests (typically 4 to 15 piezometers) over depths of 10 to 80 m. Data from piezometer nests generally have poor vertical resolution (meters), raising questions about their capacity to reveal the impact of finer scale heterogeneities such as permeable sand bodies or fractured till zones on solute transport. Here, we used high-resolution (30-cm) depth profiles of δD and δ¹⁸O from two continuously cored boreholes in a till aquitard to provide new insights into the effects of sand bodies on solute transport. High-resolution core-derived profiles indicate that such heterogeneities can cause major deviations from one-dimensional diffusion profiles. Further, comparison of piezometer-measured values with best-fit diffusion trends shows subtle deviations, suggesting the presence of heterogeneities that should not be ignored. High-resolution profiles also more clearly defined the contact between the highly fractured oxidized zone and the underlying unoxidized zone than the piezometers.     

Simulating conservative tracers in fractured till under realistic timescales

Discrete-fracture and dual-porosity models are infrequently used to simulate solute transport through fractured unconsolidated deposits, despite their more common application in fractured rock where distinct flow regimes are hypothesized. In this study, we apply four fracture transport models--the mobile-immobile model (MIM), parallel-plate discrete-fracture model (PDFM), and stochastic and deterministic discrete-fracture models (DFMs)--to demonstrate their utility for simulating solute transport through fractured till. Model results were compared to breakthrough curves (BTCs) for the conservative tracers potassium bromide (KBr), pentafluorobenzoic acid (PFBA), and 1,4-piperazinediethanesulfonic acid (PIPES) in a large-diameter column of fractured till. Input parameters were determined from independent field and laboratory methods. Predictions of Br BTCs were not significantly different among models; however, the stochastic and deterministic DFMs were more accurate than the MIM or PDFM when predicting PFBA and PIPES BTCs. DFMs may be more applicable than the MIM for tracers with small effective diffusion coefficients (De) or for short timescales due to differences in how these models simulate diffusion or incorporate heterogeneities by their fracture networks. At large scales of investigation, the more computationally efficient MIM and PDFM may be more practical to implement than the three-dimensional DFMs, or a combination of model approaches could be employed. Regardless of the modeling approach used, fractures should be incorporated routinely into solute transport models in glaciated terrain.     

Scale‐dependent Poiseuille flow alternatively explains enhanced dispersion in geothermal environments

Fluid flow exerts a critical impact on the convection of thermal energy in geological media, whereas heat transport in turn affects fluid properties, including fluid dynamic viscosity and density. The interplay of flow and heat transport also affects solute transport. To unravel these complex coupled flow, heat, and solute transport processes, here, we present a theory for the idealized scale‐dependent Poiseuille flow model considering a constant temperature gradient (?T) along a single fracture, where fluid dynamic viscosity connects with temperature via an exponential function. The idealized scale‐dependent model is validated based on the solutions from direct numerical simulations. We find that the hydraulic conductivity (K) of the Poiseuille flow either increases or decreases with scales depending on ?T > 0°C/m or ?T < 0°C/m, respectively. Indeed, the degree of changes in K depends on the magnitude of ?T and fracture length. The scale‐dependent model provides an alternative explanation for the well‐known scale‐dependent transport problem, for example, the dispersion coefficient increases with travel distance when ?T > 0°C/m according to the Taylor dispersion theory, because K (or equivalently flux through fractures) scales with fracture length. The proposed theory unravels intertwined interactions between flow and transport processes, which might shed light on understanding many practical geophysical problems, for example, geothermal energy exploration.     

Effect of permeability variations on solute transport in highly heterogeneous porous media

The effect of aquifer heterogeneity on flow and solute transport in two-dimensional isotropic porous media was analyzed using the Monte Carlo method. The two-dimensional logarithmic permeability (ln K) was assumed to be a non-stationary random field with its increments being a truncated fractional Lévy motion (fLm). The permeability fields were generated using the modified successive random additions (SRA) algorithm code SRA3DC [http://www.iamg.org/CGEditor/index.htm]. The velocity and concentration fields were computed respectively for two-dimensional flow and transport with a pulse input using the finite difference codes of MODFLOW 2000 and MT3DMS. Two fLm control parameters, namely the width parameter (C) and the Lévy index (α), were varied systematically to examine their effect on the resulting permeability, flow velocity and concentration fields. We also computed the first- and second-spatial moments, the dilution index, as well as the breakthrough curves at different control planes with the corresponding concentration fields. In addition, the derived breakthrough curves were fitted using the continuous time random walk (CTRW) and the traditional advection-dispersion equation (ADE). Results indicated that larger C and smaller α both led to more heterogeneous permeability and velocity fields. The Lévy-stable distribution of increments in ln K resulted in a Lévy-stable distribution of increments in logarithm of the velocity (ln v). Both larger C and smaller α created sharper leading edges and wider tailing edges of solute plumes. Furthermore, a relatively larger amount of solute still remained in the domain after a relatively longer time transport for smaller α values. The dilution indices were smaller than unity and increased as C increased and α decreased. The solute plume and its second-spatial moments increased as C increased and α decreased, while the first-spatial moments of the solute plume were independent of C and α values. The longitudinal macrodispersivity was scale-dependent and increased as a power law function of time. Increasing C and decreasing α both resulted in an increase in longitudinal macrodispersivity. The transport in such highly heterogeneous media was slightly non-Gaussian with its derived breakthrough curves being slightly better fitted by the CTRW than the ADE, especially in the early arrivals and late-time tails.     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.     

Temporal variability of solute transport under vadose zone conditions

The heterogeneity of the solute flux field in the horizontal plane at the field scale has been documented in several field studies. On the other hand, little information is available on the persistence of certain solute transport scenarios over consecutive infiltration cycles. This study was initiated to analyse the recurrence of solute leaching behaviour as estimated in two soil column tests emphasizing the preferential flow phenomenon. Twenty-four small-sized soil samples were subjected to two consecutive unsaturated steady-state flow leaching experiments with bromide as tracer. Observed breakthrough curves (BTCs) were analysed by the method of moments and by the advection–dispersion equation (ADE) to classify solute behaviour. Frequency distributions of the parameters indicating the solute velocity were heavily skewed or bimodal, reflecting the broad variability of the leaching scenarios, including some with pronounced preferential solute breakthrough. Exclusion of the preferential flow columns from our calculations revealed an average amount of 37% of immobile water. The large-scale BTCs derived from assembling the individual concentration courses of each run showed similar features, such as an early bromide breakthrough. However, two distinct apices, viz. one preferential and one matrix, were observed only in the first run, whereas the concentration decrease between the peaks was missing from the second run. A change in soil structure with continuous leaching was presumed to modify the interplay of the various flow domains, thereby altering the spreading of the BTCs. Correlation analysis between parameters of both tests suggests that preferential transport conditions are likely to occur at the same locations in the field over several infiltration cycles, whereas the ‘classical’ or expected matrix flow is time variant and therefore seems to be hardly predictable. © 1998 John Wiley & Sons, Ltd.     

Characterizing heterogeneous soil water flow and solute transport using information measures

Heterogeneous water flow and solute transport in soils are an important phenomenon and difficult to be characterized. The objectives of this study were to investigate the heterogeneity of solute transport related to heterogeneous soil water flow using dye infiltration experiments, and to characterize heterogeneous water flow and solute transport in soils using the information theory. Field experiments of dye infiltration were performed in four plots. Various information measures were applied to characterize information content and complexity of water flow and solute transport in soils. Information contents and complexities of the maximum and apparent infiltration depths, and the mean and standard deviation of concentrations in the vertical direction of the plots were calculated. More heterogeneous processes of soil water flow and transport result in higher information/complexity values. The probability distributions of mean concentration were similar to those of the corresponding apparent infiltration depths for the plots, indicating that heterogeneity of dye concentrations was closely related to that of soil water flow. However, the range of information entropy and complexity of the water flow sequences was much narrower than that of the sequences of the concentrations. The results suggested that the transport processes were more heterogeneous than the water flow processes. Compared with the probability distributions of flow parameters, the information measures appeared to be a more versatile tool to describe flow and transport heterogeneities in soils.     

Multi-scale heterogeneity of soil moisture following snow thawing in Haloxylon ammodendron shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.

     

Characterising deep vadose zone water movement and solute transport under typical irrigated cropland in the North China Plain

Understanding the dynamics and mechanisms of soil water movement and solute transport is essential for accurately estimating recharge rates and evaluating the impacts of agricultural activities on groundwater resources. In a thick vadose zone (0–15 m) under irrigated cropland in the piedmont region of the North China Plain, soil water content, matric potential, and solute concentrations were measured. Based on these data, the dynamics of soil water and solutes were analysed to investigate the mechanisms of soil water and solute transport. The study showed that the 0–15‐m vadose zone can be divided into three layers: an infiltration and evaporation layer (0–2 m), an unsteady infiltration layer (2–6 m), and a quasi‐steady infiltration layer (6–15 m). The chloride, nitrate, and sulphate concentrations all showed greater variations in the upper soil layer (0–1 m) compared to values in the deep vadose zone (below 2 m). The average concentrations of these three anions in the deep vadose zone varied insignificantly with depth and approached values of 125, 242, and 116 mg/L. The accumulated chloride, sulphate, and nitrate were 2,179 ± 113, 1,760 ± 383, and 4,074 ± 421 kg/ha, respectively. The soil water potential and solute concentrations indicated that uniform flow and preferential flow both occurred in the deep vadose zone, and uniform flow was the dominant mechanism of soil water movement in this study. The piston‐like flow velocity of solute transport was 1.14 m per year, and the average value of calculated leached nitrate nitrogen was 107 kg/ha?year below the root zone. The results can be used to better understand recharge processes and improve groundwater resources management.     

Test of statistical means for the extrapolation of soil depth point information using overlays of spatial environmental data and bootstrapping techniques

Hydrological modelling depends highly on the accuracy and uncertainty of model input parameters such as soil properties. Since most of these data are field surveyed, geostatistical techniques such as kriging, classification and regression trees or more sophisticated soil‐landscape models need to be applied to interpolate point information to the area. Most of the existing interpolation techniques require a random or regular distribution of points within the study area but are not adequate to satisfactorily interpolate soil catena or transect data. The soil landscape model presented in this study is predicting soil information from transect or catena point data using a statistical mean (arithmetic, geometric and harmonic mean) to calculate the soil information based on class means of merged spatial explanatory variables. A data set of 226 soil depth measurements covering a range of 0–6·5 m was used to test the model. The point data were sampled along four transects in the Stubbetorp catchment, SE‐Sweden. We overlaid a geomorphology map (8 classes) with digital elevation model‐derived topographic index maps (2–9 classes) to estimate the range of error the model produces with changing sample size and input maps. The accuracy of the soil depth predictions was estimated with the root mean square error (RMSE) based on a testing and training data set. RMSE ranged generally between 0·73 and 0·83 m ± 0·013 m depending on the amount of classes the merged layers had, but were smallest for a map combination with a low number of classes predicted with the harmonic mean (RMSE = 0·46 m). The results show that the prediction accuracy of this method depends on the number of point values in the sample, the value range of the measured attribute and the initial correlations between point values and explanatory variables, but suggests that the model approach is in general scale invariant. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi-scale heterogeneity of soil moisture following snow thawing in <Emphasis Type="Italic">Haloxylon ammodendron</Emphasis> shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.     

Multi-scale heterogeneity of soil moisture following snow thawing in Haloxylon ammodendron shrubland

Spatial variation of soil moisture after snow thawing in South Gurbantunggut was quantitatively studied using ANOVA and geostatistics at various scales. The results show that the soil moisture heterogeneity varies along with spatial scales. At the shrub individual scale, there is a gradient in soil moisture from shrub-canopied area to canopy margin and to the interspaces between shrubs. At the community scale, soil moisture is highly autocorrelated and the semivariogram is fitted as spherical model, with an 89.6% structural variance and a range of 4.02 m. In addition, Kringing map indicates that the soil moisture distribution pattern after snow thawing is highly consistent with the shrub patch pattern. At the typical inter-dune transect scale, soil moisture presents a pattern of high value at inter-dune depression and low value at dune, and this variation is fitted as Gaussian model with a structural variance of 95.8% and a range of 66.16 m. The range is comparable with the scale of topography zoning, suggesting that the topography pattern controls the pattern of snowmelt at this scale. The evidence indicates that the heterogeneity of soil moisture at various scales is controlled by various land surface processes after snow thawing. For Gurbantunggut Desert, the spatial heterogeneity of snowmelt at various scales is ecologically valuable, because it promotes the utilization efficiency of the snowmelt for the desert vegetation.     

Stochastic evaluation of subsurface contaminant discharges under physical,chemical, and biological heterogeneities

A finite element 2D Monte Carlo approach is used to evaluate the sensitivity of groundwater contaminant discharges to a Damkohler number ω and spatial variability in aquifer hydraulic conductivity, initial microbial biomass concentrations, and electron acceptor/donor concentrations. Bioattenuation is most sensitive to spatial variations in incipient biomass and critical electron donors/acceptors for ω ≥ 1 (i.e., when pore-water residence times are high compared to the time needed for microbial growth or contaminant attenuation). Under these conditions, critical reaction processes can become substrate-limited at multiple locations throughout the aquifer; which in turn increases expected contaminant discharges and their uncertainties at monitored transects. For ω ≤ 0.2, contaminant discharge is not sensitive to incipient biomass variations. Physical heterogeneities expedite plume arrival and delay departure at transects and in turn attenuate peak discharges but do not affect cumulative contaminant discharges. Physical heterogeneities do, however, induce transect mass discharge variances that are bimodal functions of time; the first peak beings consistently higher. A simple stream tube model is invoked to explain the occurrence of peaks in contaminant discharge variance.     

The scaling characteristics of soil parameters: From plot scale heterogeneity to subgrid parameterization

The variation in soil texture, surface moisture or vertical soil moisture gradient in larger scale atmospheric models may lead to significant variations in simulated surface fluxes of water and heat. The parameterization of soil moisture fluxes at spatial scales compatible with the grid size of distributed hydrological models and mesoscale atmospheric models ( 100 km²) faces principal problems which relate to the underlying microscopic or field scale heterogeneity in soil characteristics.

The most widely used parameterization in soil hydrology, the Darcy-Richards (DR) equation, is gaining increasing importance in mesoscale and climate modelling. This is mainly due to the need to introduce plant-interactive soil water depletion and stomatal conductance parameterizations and to improve the calculation of deep percolation and runoff. Covering a grid of several hundreds of square kilometres, the DR parameterization in soil-vegetation-atmosphere-transfer schemes (SVATs) is assumed to be scale-invariant. The parameters describing the non-linear, area-average soil hydraulic functions in this scale-invariant DR-equation should be treated as calibration-parameters, which do not necessarily have a physical meaning. The saturated hydraulic conductivity is one of the soil parameters to which the models show very high sensitivity. It is shown that saturated hydraulic conductivity can be scaled in both vertical and horizontal directions for large flow domains.

In this paper, a distinction is made between effective and aggregated soil parameters. Effective parameters are defined as area-average values or distributions over a domain with a single, distinct textural soil type. They can be obtained by scaling or inverse modelling. Aggregated soil parameters represent grid-domains with several textural soil types. In soil science dimensional methods have been developed to scale up soil hydraulic characteristics. With some specific assumptions, these techniques can be extrapolated from classical field-scale problems in soil heterogeneity to larger domains, compatible with the grid-size of large scale models. Particularly promising is the estimation of effective soil hydraulic parameters from area averaging measurements through inverse modelling of the unsaturated flow.

Techniques to scale and aggregate the soil characteristics presented in this paper qualify for direct or indirect use in large scale meteorological models. One of the interesting results is the effective behaviour of the reference curve, which can be obtained from similar media scaling. If the conclusions of this paper survive further studies, a relatively simple method will become available to parameterize soil variability at large scales. The inverse technique is found to provide effective soil parameters which perform well in predicting both the area-average evaporation and the area-average soil moisture fluxes, such as subsurface runoff. This is not the case for aggregated soil parameters. Obtained from regression relationships between soil textural composition and hydraulic characteristics, these aggregated parameters predict evaporation fluxes well, but fail to predict water balance terms such as percolation and runoff. This is a serious drawback which could eventually hamper the improvement of the representation of the hydrological cycle in mesoscale atmospheric models and in GCMs.